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Research Highlights

Testing Identifying Assumptions in Fuzzy Regression Discontinuity Designs (with Yoichi Arai, Toru Kitagawa, Ismael Mourifié, and Yuanyuan Wan, accepted by QUANTITATIVE ECONOMICS)

  • Author Yoichi Arai
    Yu-Chin Hsu
    Toru Kitagawa
    Ismael Mourifié
    Yuanyuan Wan
  • Abstract We propose a new specification test for assessing the validity of fuzzy regression discon-tinuity designs (FRD-validity). We derive a new set of testable implications, characterized by a set ofinequality restrictions on the joint distribution of observed outcomes and treatment status at the cut-off. We show that this new characterization exploits all the information in the data useful for detectingviolations of FRD-validity. Our approach differs from, and complements existing approaches that testcontinuity of the distributions of running variables and baseline covariates at the cut-off since oursfocuses on the distribution of the observed outcome and treatment status. We show that the proposedtest has appealing statistical properties. It controls size in large sample uniformly over a large class ofdistributions, is consistent against all fixed alternatives, and has non-trivial power against some localalternatives. We apply our test to evaluate the validity of two FRD designs. The test does not reject the FRD-validity in the class size design studied by Angrist and Lavy (1999) and rejects in the insurancesubsidy design for poor households in Colombia studied by Miller, Pinto, and Vera-Hernández (2013) for some outcome variables, while existing density tests suggest the opposite in each of the cases.
  • Link https://www.cemmap.ac.uk/wp-content/uploads/2020/08/CWP5018.pdf(Open New Window)